• Title/Summary/Keyword: 2-Opt Algorithm

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Optimization of the Travelling Salesman Problem Using a New Hybrid Genetic Algorithm

  • Zakir Hussain Ahmed;Furat Fahad Altukhaim;Abdul Khader Jilani Saudagar;Shakir Khan
    • International Journal of Computer Science & Network Security
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    • v.24 no.3
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    • pp.12-22
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    • 2024
  • The travelling salesman problem is very famous and very difficult combinatorial optimization problem that has several applications in operations research, computer science and industrial engineering. As the problem is difficult, finding its optimal solution is computationally very difficult. Thus, several researchers have developed heuristic/metaheuristic algorithms for finding heuristic solutions to the problem instances. In this present study, a new hybrid genetic algorithm (HGA) is suggested to find heuristic solution to the problem. In our HGA we used comprehensive sequential constructive crossover, adaptive mutation, 2-opt search and a new local search algorithm along with a replacement method, then executed our HGA on some standard TSPLIB problem instances, and finally, we compared our HGA with simple genetic algorithm and an existing state-of-the-art method. The experimental studies show the effectiveness of our proposed HGA for the problem.

A Minimum Expected Length Insertion Algorithm and Grouping Local Search for the Heterogeneous Probabilistic Traveling Salesman Problem (이종 확률적 외판원 문제를 위한 최소 평균거리 삽입 및 집단적 지역 탐색 알고리듬)

  • Kim, Seung-Mo;Choi, Ki-Seok
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.33 no.3
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    • pp.114-122
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    • 2010
  • The Probabilistic Traveling Salesman Problem (PTSP) is an important topic in the study of traveling salesman problem and stochastic routing problem. The goal of PTSP is to find a priori tour visiting all customers with a minimum expected length, which simply skips customers not requiring a visit in the tour. There are many existing researches for the homogeneous version of the problem, where all customers have an identical visiting probability. Otherwise, the researches for the heterogeneous version of the problem are insufficient and most of them have focused on search base algorithms. In this paper, we propose a simple construction algorithm to solve the heterogeneous PTSP. The Minimum Expected Length Insertion (MELI) algorithm is a construction algorithm and consists of processes to decide a sequence of visiting customers by inserting the one, with the minimum expected length between two customers already in the sequence. Compared with optimal solutions, the MELI algorithm generates better solutions when the average probability is low and the customers have different visiting probabilities. We also suggest a local search method which improves the initial solution generated by the MELI algorithm.

Performance Comparison of Discrete Particle Swarm Optimizations in Sequencing Problems (순서화 문제에서 01산적 Particle Swarm Optimization들의 성능 비교)

  • Yim, D.S.
    • Journal of Korean Society of Industrial and Systems Engineering
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    • v.33 no.4
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    • pp.58-68
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    • 2010
  • Particle Swarm Optimization (PSO) which has been well known to solve continuous problems can be applied to discrete combinatorial problems. Several DPSO (Discrete Particle Swarm Optimization) algorithms have been proposed to solve discrete problems such as traveling salesman, vehicle routing, and flow shop scheduling problems. They are different in representation of position and velocity vectors, operation mechanisms for updating vectors. In this paper, the performance of 5 DPSOs is analyzed by applying to traditional Traveling Salesman Problems. The experiment shows that DPSOs are comparable or superior to a genetic algorithm (GA). Also, hybrid PSO combined with local optimization (i.e., 2-OPT) provides much improved solutions. Since DPSO requires more computation time compared with GA, however, the performance of hybrid DPSO is not better than hybrid GA.

Visual Object Tracking Fusing CNN and Color Histogram based Tracker and Depth Estimation for Automatic Immersive Audio Mixing

  • Park, Sung-Jun;Islam, Md. Mahbubul;Baek, Joong-Hwan
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.14 no.3
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    • pp.1121-1141
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    • 2020
  • We propose a robust visual object tracking algorithm fusing a convolutional neural network tracker trained offline from a large number of video repositories and a color histogram based tracker to track objects for mixing immersive audio. Our algorithm addresses the problem of occlusion and large movements of the CNN based GOTURN generic object tracker. The key idea is the offline training of a binary classifier with the color histogram similarity values estimated via both trackers used in this method to opt appropriate tracker for target tracking and update both trackers with the predicted bounding box position of the target to continue tracking. Furthermore, a histogram similarity constraint is applied before updating the trackers to maximize the tracking accuracy. Finally, we compute the depth(z) of the target object by one of the prominent unsupervised monocular depth estimation algorithms to ensure the necessary 3D position of the tracked object to mix the immersive audio into that object. Our proposed algorithm demonstrates about 2% improved accuracy over the outperforming GOTURN algorithm in the existing VOT2014 tracking benchmark. Additionally, our tracker also works well to track multiple objects utilizing the concept of single object tracker but no demonstrations on any MOT benchmark.

The Maximum Scatter Travelling Salesman Problem: A Hybrid Genetic Algorithm

  • Zakir Hussain Ahmed;Asaad Shakir Hameed;Modhi Lafta Mutar;Mohammed F. Alrifaie;Mundher Mohammed Taresh
    • International Journal of Computer Science & Network Security
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    • v.23 no.6
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    • pp.193-201
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    • 2023
  • In this paper, we consider the maximum scatter traveling salesman problem (MSTSP), a travelling salesman problem (TSP) variant. The problem aims to maximize the minimum length edge in a salesman's tour that travels each city only once in a network. It is a very complicated NP-hard problem, and hence, exact solutions can be found for small sized problems only. For large-sized problems, heuristic algorithms must be applied, and genetic algorithms (GAs) are found to be very successfully to deal with such problems. So, this paper develops a hybrid GA (HGA) for solving the problem. Our proposed HGA uses sequential sampling algorithm along with 2-opt search for initial population generation, sequential constructive crossover, adaptive mutation, randomly selected one of three local search approaches, and the partially mapped crossover along with swap mutation for perturbation procedure to find better quality solution to the MSTSP. Finally, the suggested HGA is compared with a state-of-art algorithm by solving some TSPLIB symmetric instances of many sizes. Our computational experience reveals that the suggested HGA is better. Further, we provide solutions to some asymmetric TSPLIB instances of many sizes.

Heterogeneous Fleet Vehicle Routing Problem with Customer Restriction using Hybrid Particle Swarm Optimization (Hybrid-PSO 해법을 이용한 수요지 제한이 있는 다용량 차량경로문제)

  • Lee, Sang-Heon;Hwang, Sun-Ho
    • Journal of Korean Institute of Industrial Engineers
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    • v.35 no.2
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    • pp.150-159
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    • 2009
  • The heterogeneous fleet vehicle routing problem(HVRP) is a variant of the classical vehicle routing problem in which customers are served by a heterogeneous fleet of vehicles with various capacities, fixed costs and variable costs. We propose a new conceptual HVRPCR(HVRP with customer restriction) model including additional customer restrictions in HVRP. In this paper, we develop hybrid particle swarm optimization(HPSO) algorithm with 2-opt and node exchange technique for HVRP. The solution representation is a n-dimensional particle for HVRP with N customers. The decoding method for this representation starts with the transformation of particle into a priority list of customer to enter route and limit of vehicle to serve each customer. The vehicle routes are then constructed based on the customer priority list and limit of vehicle to serve. The proposed algorithm is tested using 8 benchmark problems and it consistently produces high-quality solutions, including new best solutions. The numerical results show that the proposed algorithm is robust and efficient.

Structural Design Optimization of Gageocho Jacket Structure Considering Unity Check (가거초 자켓 구조물의 허용응력비를 고려한 구조 최적설계)

  • Kim, Byungmo;Ha, Seung-Hyun
    • Journal of the Computational Structural Engineering Institute of Korea
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    • v.34 no.4
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    • pp.205-212
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    • 2021
  • Offshore jacket structures generally comprise steel members, and the safety standard for jacket structures typically focuses on the steel components. However, large amounts of concrete grouting is filled in the legs of the Gageocho jacket structure to aid in the recovery from typhoon damage. This paper proposes a safe and lightweight design for the Gageocho ocean research station comprising steel members instead of large amounts of concrete reinforcement in the legs. Based on the actual design, the structural members are grouped according to their functional roles, and the inner diameter of the cross-section in each design group is defined as a design variable. Structural optimization is carried out using a genetic algorithm to minimize the total weight of the structure. To satisfy the conservative safety standards in the offshore field, both the maximum stress and the unity check criteria are considered as design constraints during optimization. For enhanced safety confidence, extreme environmental conditions are assumed. The maximum marine attachment thickness and the section erosion in the splash zone are applied. Additionally, the design load is defined as the force induced by extreme waves, winds, and currents aligned in the same direction. All the loading directions surrounding the structure are considered to design the structure in a balanced and safe manner. As a result, compared with the current structure, the proposed structure features a 45% lighter design, satisfying the strict offshore safety criteria.

Energy Performance Variation of Solar Water Heating System by LCC Optimization in an Office Building (사무소 건물 태양열급탕시스템의 LCC 최적화에 따른 에너지성능 변화 분석)

  • Ko, Myeong-Jin;Choi, Doo-Sung;Chang, Jae-Dong;Kim, Yong-Shik
    • Journal of the Korean Solar Energy Society
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    • v.31 no.2
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    • pp.89-98
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    • 2011
  • This study examined the energy performance according to the main design parameters of a solar water heating system for an office building using the life cycle cost (LCC) optimization simulations. The LCC optimization simulations of the system were conducted with TRNSYS and GenOpt employing the Hooke-Jeeves algorithm for cases where water temperature was $60^{\circ}C$ and $50^{\circ}C$. The results showed that for water temperature at $60^{\circ}C$ and $50^{\circ}C$ the global radiation incident on the collector could be decreased by 16.98% and 28.52%, collector useful energy gain could be decreased by 15.04% and 22.59%, energy to load from storage tank could be decreased by 10.86% and 18.06% and AH energy to load could be increased by 16.86% and 38.50% respectively compared to a non-optimized system. The annual average collection efficiency of the collector was increased by 0.88% for $60^{\circ}C$ and 2.78% for $50^{\circ}C$ because of increase of collector slope and decrease of the mass flow rate per collector area. The annual average efficiency of the system was increased by 1.74% and 3.47% compared to the basis system. However, the annual solar fraction of the system was decreased by 6.68% for $60^{\circ}C$ and 11.26% for $50^{\circ}C$ due to decrease of collector area and storage tank volume.

Hybrid Heuristic Applied by the Opportunity Time to Solve the Vehicle Routing and Scheduling Problem with Time Window (시간 제약을 가지는 차량 경로 스케줄링 문제 해결을 위한 기회시간 반영 하이브리드 휴리스틱)

  • Yu, Young-Hoon;Cha, Sang-Jin;Jo, Geun-Sik
    • Journal of Intelligence and Information Systems
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    • v.15 no.3
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    • pp.137-150
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    • 2009
  • This paper proposes the hybrid heuristic method to apply the opportunity time to solve the vehicle routing and scheduling problem with time constraints(VRSPTW). The opportunity time indicates the idle time which remains after the vehicle performs the unloading service required by each customer's node. In this proposed heuristic, we add the constraints to VRSPTW model for the opportunity time. We also obtain the initial solution by applying the cost evaluation function to the insertion strategy considering the opportunity time. In addition, we improve the former result by applying the opportunity time to the tabu search strategy by swapping the customer's node. Finally, we suggest the construction strategies of initial routing which can efficiently acquire the nearest optimal solution from various types of data in terms of geographical condition, scheduling horizon and vehicle capacity. Our experiment show that our heuristic can get the nearest optimal solution more efficiently than the Solomon's I1 heuristic.

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Classification of Magnetic Resonance Imagery Using Deterministic Relaxation of Neural Network (신경망의 결정론적 이완에 의한 자기공명영상 분류)

  • 전준철;민경필;권수일
    • Investigative Magnetic Resonance Imaging
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    • v.6 no.2
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    • pp.137-146
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    • 2002
  • Purpose : This paper introduces an improved classification approach which adopts a deterministic relaxation method and an agglomerative clustering technique for the classification of MRI using neural network. The proposed approach can solve the problems of convergency to local optima and computational burden caused by a large number of input patterns when a neural network is used for image classification. Materials and methods : Application of Hopfield neural network has been solving various optimization problems. However, major problem of mapping an image classification problem into a neural network is that network is opt to converge to local optima and its convergency toward the global solution with a standard stochastic relaxation spends much time. Therefore, to avoid local solutions and to achieve fast convergency toward a global optimization, we adopt MFA to a Hopfield network during the classification. MFA replaces the stochastic nature of simulated annealing method with a set of deterministic update rules that act on the average value of the variable. By minimizing averages, it is possible to converge to an equilibrium state considerably faster than standard simulated annealing method. Moreover, the proposed agglomerative clustering algorithm which determines the underlying clusters of the image provides initial input values of Hopfield neural network. Results : The proposed approach which uses agglomerative clustering and deterministic relaxation approach resolves the problem of local optimization and achieves fast convergency toward a global optimization when a neural network is used for MRI classification. Conclusion : In this paper, we introduce a new paradigm to classify MRI using clustering analysis and deterministic relaxation for neural network to improve the classification results.

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